We investigate coherent exciton transitions in GaAs/Al(x)Ga1-xAs quantum wells using subpicosecond four-wave-mixing spectroscopy. In a first part, we show that the four-wave-mixing lineshape deviates considerably from earlier predictions when the detailed structure of the excitons is taken into account, and we study the density dependence and excitation energy dependence in detail. In a second part, we discuss the observation of quantum beats due to the coherent superposition of different excitonic transitions and show how the analysis of the lineshape can yield information about relaxation processes.